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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Statistics

NDA 2021 · Mathematics · Statistics

If ∑_ i=1 ^ 10 x_i=110 and ∑_ i=1 ^ 10 x_i^2=1540 then what is the...

If ∑i=110xi=110\sum_{i=1}^{10} x_i=110 and ∑i=110xi2=1540\sum_{i=1}^{10} x_i^2=1540 then what is the variance?

Options

  1. A22
  2. B22
  3. C44
  4. D55

Correct answer

B. 22

Step-by-step solution

Here, ∑i=110xi=110\sum_{i=1}^{10} x i=110 and ∑i=110xi2=1540\sum_{i=1}^{10} x i^2=1540 Variance =1N∑i=110xi2−(1N∑i=110xi)2=154010−(11010)2=154−121=33∴ variance =33\begin{aligned} & \text{ Variance }=\frac{1}{N} \sum_{i=1}^{10} x i^2-\left(\frac{1}{N} \sum_{i=1}^{10} x i\right)^2 \\ & =\frac{1540}{10}-\left(\frac{110}{10}\right)^2=154-121=33 \\ & \therefore \text{ variance }=33 \end{aligned}$$
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